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Abstract:

The figure is fixed in a given position. If peaks are seen in the
positive Y direction, the minimum value of the difference in height
between the spectrum and the figure in the range where the figure is
present on the X-axis. The minimum value and the height of the figure at
the reference point are added. The figure is moved within a range
containing the reference point, and the minimum value of the difference
in height between the spectrum and the figure is added to the height of
the figure at the reference point, at each point on the figure. A maximum
value L.sub.(xi) of the calculated values is obtained, and the maximum
value L.sub.(xi) is obtained as a baseline value at the X coordinate of
the reference point.

Claims:

1-5. (canceled)

6. A baseline setting method for setting the baseline of a measured curve
plotted on a reference axis X and a measured value axis Y extending in a
direction orthogonal to the reference axis X, the measured curve having a
single measured value yi identified with respect to a point xi
on the reference axis X, the baseline setting method comprising; moving a
figure selected among a semicircle, a semi-ellipse, or a quadratic curve
on the axis X; if peaks of the measured curve are seen in the negative Y
direction, (i) specifying a semicircle or semi-ellipse CXi centered
on the reference axis X and an X radius R, expressed by
x2+a2y2=r2 y≦0
fXi(x)={(r2-x2)1/2}/a or (ii) specifying a quadratic
curve CXi centered on the reference axis X, expressed by
y=a(x-b)2+c under the conditions: b-r≦x≦b+r
M≧W a>0 f(x)=a(x-b)2+c where W is the full width at
half maximum of a peak having the greatest peak width among a plurality
of peaks seen in the measured curve, if the peaks of the measured curve
are seen in the positive Y direction; comparing individual points
(xi-r, fXi(xi-r)) to (xi+r, fXi(xi+r)) of
the semicircle or semi-ellipse CXi centered at (xi, 0) with the
corresponding points (xi-r, yXi-r) to (xi+r, yXi+r)
on the measured curve to calculate l Xi - r = f Xi (
x i - r ) - y Xi - r l Xi + r = f Xi ( x
i + r ) - y Xi + r ##EQU00026## and to specify the minimum
value of lXi-r to lXi+r as l.sub.(Xi)min; specifying the
minimum value of f Xi - r ( x i ) - l ( x i -
r ) min f Xi + r ( x i ) - l ( x i + r
) min ##EQU00027## obtained with respect to each of semicircles,
semi-ellipses, or a quadratic curve CXi--r to CXi+r centered at
(xi-r, 0) to (xi+r, 0), as L.sub.(xi); setting a baseline point
(xi, L.sub.(xi)) corresponding to a specific point (xi,
yi) on the measured curve; and connecting the baseline points
corresponding to the individual points on the measured curve, to form a
baseline.

7. A baseline setting method for a measured curve plotted on a reference
axis X and a measured value axis Y extending in a direction orthogonal to
the reference axis X, the measured curve having a single measured value
yi identified with respect to each point xi on the reference
axis X, the baseline setting method comprising the steps of: specifying a
semicircle or semi-ellipse Cxi centered on the reference axis X and
an X radius, expressed by x2+a2y2=r2 y≦0
fXi(x)={(r2-x2)1/2}/a if peaks of the measured curve
are seen in the negative Y direction; comparing individual points
(xi-r, fXi(xi-r)) to (xi+r, fXi(xi+r)) of
the semicircle or semi-ellipse CXi centered at (xi, 0) with the
corresponding points (xi-r, yXi-r) to (xi+r, yXi+r)
on the measured curve to calculate l Xi - r = f Xi (
x i - r ) - y Xi - r l Xi + r = f Xi ( x
i + r ) - y Xi + r ##EQU00028## and to specify the minimum
value of lXi-r to lXi+r as l.sub.(Xi)min; specifying the
minimum value of f Xi - r ( x i ) - l ( x i -
r ) min f Xi + r ( x i ) - l ( x i + r
) min ##EQU00029## obtained with respect to each of semicircles
or semi-ellipses CXi-r to CXi+r centered at (xi-r, 0) to
(xi+r, 0), as L.sub.(xi)); setting a baseline point (xi,
L.sub.(xi)) corresponding to a specific point (xi, yi) on the
measured curve; and connecting the baseline points corresponding to the
individual points on the measured curve, to form a baseline.

8. A baseline setting method for a measured curve plotted on a reference
axis X and a measured value axis Y extending in a direction orthogonal to
the reference axis X, the measured curve having a single measured value
yi identified with respect to each point xi on the reference
axis X, the baseline setting method comprising the steps of: specifying a
quadratic curve DXi centered on the reference axis X, expressed by
y=a(x-b)2+c under the conditions b-M≦x≦b+M
M≧W a>0 f(x)=a(x-b)2+c where W is the full width at
half maximum of a peak having the greatest peak width among a plurality
of peaks seen in the measured curve, if the peaks of the measured curve
are seen in the negative Y direction; comparing individual points
(xi-M, fXi(xi-M)) to (xi+M, fXi(xi+M)) of
the quadratic curve DXi having its vertex at (xi, c) (xi=b
at the beginning of the measurement) with the corresponding points
(xi-M, yXi-M) to (xi+M, yXi+M) on the measured curve
to calculate l Xi - M = f Xi ( x i - M ) - y Xi
- M l Xi + M = f Xi ( x i + M ) - y Xi +
M ##EQU00030## and to specify the minimum value of lXi-M to
lXi+M as l.sub.(Xi)min; specifying the minimum value of f
Xi - M ( x i ) - l ( x i - M ) min f
Xi + M ( x i ) - l ( x i + M ) min ##EQU00031##
obtained with respect to each of quadratic curves DXi-M to
DXi+M with their vertices at (xi-M, c) to (xi+M, c), as
L.sub.(xi); setting a baseline point (xi, L.sub.(xi)) corresponding
to a specific point (xi, yi) on the measured curve; setting
baseline points corresponding to the individual points on the measured
curve by moving the vertex in the X direction; and connecting the
baseline points to form a baseline.

9. The baseline setting method of claim 7, wherein the X radius R of the
semicircle or semi-ellipse CXi is specified to be at least twice the
full width at half maximum, W, of a peak having the greatest peak width
among a plurality of peaks seen in the measured curve.

Description:

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention relates to baseline setting methods, and more
specifically, to an improvement of a baseline estimation method.

[0003] 2. Description of the Related Art

[0004] In spectrum measurement by an infrared spectrophotometer or the
like, the wavelength or wavenumber is indicated on the reference axis
(X-axis), and the absorbance, reflectance, or the like is indicated on
the Y-axis, in usual cases. Then, measured values are plotted with
respect to points on the reference axis.

[0005] While the absorbance, reflectance, or the like is plotted when the
wavelength is changed, a narrow mountain, known as a peak, appears in the
spectrum. This occurs because the atom or molecule has the property of
emitting or absorbing light at a specific wavelength.

[0006] However, the baseline of the spectrum depends on the
characteristics of the instrument used to take the spectrum or the
environment in which the spectrum measurement is being carried out.
Sometimes, the occurrence of fluorescence and the like may also influence
the baseline.

[0007] Therefore, the baseline setting for the spectrum and spectrum data
correction based on the set baseline are essential techniques in spectrum
data processing.

[0008] In particular, in infrared transmission spectrum measurement of a
specimen having a rough surface or a specimen containing a pulverized
inorganic compound, dispersion occurs on the surface of the specimen or
in the specimen. This has a great influence on light with a short
wavelength and can lower the transmission spectrum (% T) in the high
wavenumber region. The ATR spectrum (% T) in the low wavenumber region of
a specimen containing carbon black has a falling tendency.

[0009] Since these spectra have a large overall height, the peaks become
relatively small, making it difficult to conduct a library search.

[0010] It is difficult to measure changes in the baseline directly, so
that those changes in the baseline must be estimated.

[0011] For example, in Japanese Unexamined Patent Application Publication
No. Hei-05-60614, a circle having a diameter not smaller than twice the
full width at half maximum of a peak, an ellipse, or the like is moved in
contact with but not intersecting the actually measured spectrum, and a
part of the track is used as the baseline.

[0012] Although conventional methods related to baseline correction such
as that described above have advantages, there are many problems in
actual use, such as high computational load and a wide range of
parameters to be specified, such as the shape and size of the figure.

[0013] A simple, low-computational-load baseline setting method that can
be used for any shape of spectrum, rising toward the right, rising toward
the left, rising in the middle, falling in the middle, or being wavy, has
been desired.

SUMMARY OF THE INVENTION

[0014] In view of the related art, it is an object of the present
invention to provide a simple, high-accuracy baseline setting method with
low computational load.

[0015] If peaks are seen in the positive Y direction, a baseline can be
specified by using a semicircle or a semi-ellipse, as described below.

[0016] A baseline setting method for a measured curve plotted on a
reference axis X and a measured value axis Y extending in a direction
orthogonal to the reference axis X, the measured curve having a single
measured value yi identified with respect to a point xi on the
reference axis X, the baseline setting method including the steps of:

[0017] specifying a semicircle or semi-ellipse Cxi centered on the
reference axis X and an X radius R, expressed by

x2+a2y2=r2

y≧0

fXi(x)={(r2-x2)1/2}/a

if peaks of the measured curve are seen in the positive Y direction;

[0018] comparing individual points (xi-r, fXi(xi-r)) to
(xi+r, fXi(xi+r)) of the semicircle or semi-ellipse
CXi centered at (xi, 0) with the corresponding points
(xi-r, yXi-r) to (xi+r, yXi+r) on the measured curve
to calculate

obtained with respect to each of semicircles or semi-ellipses CXi-r
to CXi+r centered at (xi-r, 0) to (xi+r, 0), as
L.sub.(xi);

[0020] setting a baseline point (xi, L.sub.(xi)) corresponding to a
specific point (xi, yi) on the measured curve; and

[0021] connecting the baseline points corresponding to the individual
points on the measured curve, to form a baseline.

[0022] If peaks are seen in the negative Y direction, a baseline can be
specified as described below.

[0023] A baseline setting method for a measured curve plotted on a
reference axis X and a measured value axis Y extending in a direction
orthogonal to the reference axis X, the measured curve having a single
measured value yi identified with respect to each point xi on
the reference axis X, the baseline setting method including the steps of:

[0024] specifying a semicircle or semi-ellipse Cxi centered on the
reference axis X and an X radius, expressed by

x2+a2y2=r2

y≦0

fXi(x)={(r2-x2)1/2}/a

if peaks of the measured curve are seen in the negative Y direction;

[0025] comparing individual points (xi-r, fXi(xi-r)) to
(xi+r, fXi(xi+r)) of the semicircle or semi-ellipse
CXi centered at (xi, 0) with the corresponding points
(xi-r, yXi-r) to (xi+r, yXi+r) on the measured curve
to calculate

obtained with respect to each of semicircles or semi-ellipses CXi-r
to CXi+r centered at (xi-r, 0) to (xi+r, 0), as
L.sub.(xi);

[0027] setting a baseline point (xi, L.sub.(xi)) corresponding to a
specific point (xi, yi) on the measured curve; and

[0028] connecting the baseline points corresponding to the individual
points on the measured curve, to form a baseline.

[0029] If peaks are seen in the positive Y direction, a baseline can be
specified by using a quadratic curve, as described below.

[0030] A baseline setting method for a measured curve plotted on a
reference axis X and a measured value axis Y extending in a direction
orthogonal to the reference axis X, the measured curve having a single
measured value yi identified with respect to each point xi on
the reference axis X, the baseline setting method including the steps of:

where W is the full width at half maximum of a peak having the greatest
peak width among a plurality of peaks seen in the measured curve, if the
peaks of the measured curve are seen in the positive Y direction;

[0032] comparing individual points (xi-M, fXi(xi-M)) to
(xi+M, fXi(xi+M)) of the quadratic curve DXi having
its vertex at (xi, c) (xi=b at the beginning of the
measurement) with the corresponding points (xi-M, yXi-M) to
(xi+M, yXi+M) on the measured curve to calculate

obtained with respect to each of quadratic curves DXi-M to
DXi+M having their vertices at (xi-M, c) to (xi+M, c), as
L.sub.(xi);

[0034] setting a baseline point (xi, L.sub.(xi)) corresponding to a
specific point (xi, yi) on the measured curve;

[0035] setting baseline points corresponding to the individual points on
the measured curve by moving the vertex in the X direction; and

[0036] connecting the baseline points to form a baseline.

[0037] If peaks are seen in the negative Y direction, a baseline can be
specified as described below.

[0038] A baseline setting method for a measured curve plotted on a
reference axis X and a measured value axis Y extending in a direction
orthogonal to the reference axis X, the measured curve having a single
measured value yi identified with respect to each point xi on
the reference axis X, the baseline setting method including the steps of:

where W is the full width at half maximum of a peak having the greatest
peak width among a plurality of peaks seen in the measured curve, if the
peaks of the measured curve are seen in the negative Y direction;

[0040] comparing individual points (xi-M, fXi(xi-M)) to
(xi+M, fXi(xi+M)) of the quadratic curve DXi having
its vertex at (xi, c) (xi=b at the beginning of the
measurement) with the corresponding points (xi-M, yXi-M) to
(xi+M, yXi+M) on the measured curve to calculate

obtained with respect to each of quadratic curves DXi-M to
DXi+M with their vertices at (xi-M, c) to (xi+M, c), as
L.sub.(xi);

[0042] setting a baseline point (xi, L.sub.(xi)) corresponding to a
specific point (xi, yi) on the measured curve;

[0043] setting baseline points corresponding to the individual points on
the measured curve by moving the vertex in the X direction; and

[0044] connecting the baseline points to form a baseline.

[0045] The track of a baseline is calculated by using a circle or ellipse,
as described below.

[0046] First, in a plane having a reference axis X and a measured value
axis Y extending orthogonally to the reference axis X, a semicircle or
semi-ellipse C centered on the reference axis X, expressed by

x2+a2y2=r2

(f(x)={(r2-x2)1/2}/a)

is specified, where y≧0 if peaks are seen in the positive Y
direction or y≦0 if peaks are seen in the negative Y direction.

[0047] The values of "a" and "r" of the semicircle or semi-ellipse C are
specified empirically.

[0048] If the X radius R of the semicircle or semi-ellipse is too small,
the baseline is set at a high position in a peak and becomes too close to
the spectrum in the peak.

[0049] Therefore, it is preferable to set the X radius R of the semicircle
or semi-ellipse C to twice the full width at half maximum, W, or greater,
where W is the full width at half maximum of a peak having the greatest
peak width among a plurality of peaks appearing in the measurement curve.

[0050] Optimum values of curvature "a" and radius "r" should be specified
with the shape and inclination of the base of the measured curve and the
peak width taken into account.

[0051] If peaks are seen in the positive Y direction, points (xi-r,
fXi(xi-r)) to (xi+r, fXi(xi+r)) on the
semicircle or semi-ellipse Cxi centered at point (xi, 0) are
compared with points (xi-r, yXi-r) to (xi+r, yXi+r)
on the spectrum. Differences lXi-r to lXi+r corresponding to
the individual points on the reference axis X are obtained as follows:

are calculated.) The minimum value among lXi-r to lXi+r is
specified as lXi(xi)min.

[0052] Then, even when the measured curve has its peak on point (xi,
0) on the X-axis, corresponding to the center of the semicircle or
semi-ellipse, if the X radius of the semicircle or semi-ellipse is
greater than the maximum peak width appearing in the spectrum,
lXi(xi)min is calculated at an off-peak position on the
X-axis.

[0053] Semicircles or semi-ellipses CXi-r to CXi+r are moved in
the range of (xi-r, 0) to (xi+r, 0),
lXi-r(xi)min to lXi+r(xi)min are obtained,
by following the procedure described above, and

[0054] The maximum value (or the minimum value, if peaks are seen in the
negative Y direction) among those values is specified as L.sub.(xi).

[0055] Then, a point (xi, L.sub.(xi)) is set as a baseline point.

[0056] As has been described above, by specifying appropriate values of
curvature "a" and radius "r" for f(x), a natural baseline can be set for
any type of spectrum having a measured curve rising toward the right,
rising toward the left, rising in the middle, falling in the middle, or
being wavy.

[0057] The point (xi, 0) is moved in the X direction, L.sub.(x(i+1))
is calculated by following the procedure described above, and a baseline
point corresponding to a specific point (x.sub.(i+1), yX(i+1)) on
the measured curve is set as (x.sub.(i+1), Lx(i+1))).

[0058] The baseline points corresponding to individual points on the
measured curve are calculated in the same way.

[0059] By connecting these baseline points, the baseline of the measured
curve can be specified.

[0060] The procedure for the baseline setting method using a quadratic
curve is almost the same as the procedure for the baseline setting method
using a semicircle or semi-ellipse. If peaks are seen in the positive Y
direction, a quadratic curve expressed by

f(x)=a(x-b)2+c

a<0

is specified in the range of

b-M≦x≦b+M.

If peaks are seen in the negative Y direction, the quadratic curve is
expressed by

f(x)=a(x-b)2+c

a>0.

[0061] First, a quadratic curve D centered at a point on the reference
axis X, represented by

y=a(x-b)2+c

(f(x)=a(x-b)2+c)

is specified, under the following conditions:

b-M≦x≦b+M

M≧W

a<0 (a>0, if peaks are seen in the negative Y direction)

where W is the full width at half maximum of a peak having the greatest
peak width among a plurality of peaks appearing in the measured curve.
The value of "a" is specified empirically. The values of "b" and "c" are
specified by the person performing the measurement as the initial
position (b, c) of the vertex of the quadratic curve D.

[0062] The value of M should not be smaller than the full width at half
maximum, W, of the peak having the greatest peak width among the
plurality of peaks appearing in the measured curve. If the value of M is
smaller, the baseline is specified at a high in a peak and becomes too
close to the spectrum in the peak.

[0063] An optimum value of "a" should be specified empirically with the
shape and inclination of the base of the measured curve and the peak
width taken into account.

[0064] If peaks are seen in the positive Y direction, individual points
(xi-r, fXi(xi-r)) to (xi+r, fXi(xi+r)) on
the quadratic curve DXi having its vertex at point (xi, c)
(xi=b at the beginning of measurement) are compared with points
(xi-r, yXi-r) to (xi+r, yXi+r) on the spectrum.
Differences lXi-r to lXi+r corresponding to the individual
points on the reference axis X are obtained as follows:

are calculated.) The minimum value among lXi-r to lXi+r is
specified as lXi(xi)min.

[0065] Then, even when the measured curve has a peak at point (xi, 0)
on the X-axis, corresponding to the vertex of the quadratic curve, if the
value of "a" is specified to set the baseline to an appropriate height
with respect to the peak and if the width (=2M) of the quadratic curve is
greater than the maximum peak width appearing on the spectrum,
lXi(xi)min is calculated at an off-peak position on the
X-axis.

[0066] Quadratic curves DXi-r to DXi+r are moved in the range of
(xi-r, 0) to (xi+r, 0), lXi-r(xi)min to
lXi+r(xi)min are obtained by following the procedure as
described above, and

[0067] The maximum value (or the minimum value, if peaks are seen in the
negative Y direction) among those values is specified as L.sub.(xi).

[0068] Then, a point (xi, L.sub.(xi)) is set as a baseline point.

[0069] As has been described above, by specifying an appropriate value of
"a" for f(x), a natural baseline can be set for any type of spectrum
having a measured curve rising toward the right, rising toward the left,
rising in the middle, falling in the middle, or being wavy.

[0070] The vertex is moved in the X direction, L.sub.(x(i+1)) is
calculated by following the procedure described above, and a baseline
point corresponding to a specific point (x.sub.(i+1), yX(i+1)) on
the measured curve is set as (x.sub.(i+1), Lx(i+1))).

[0071] The baseline points corresponding to the individual points on the
measured curve are calculated in the same way.

[0072] By connecting these baseline points, the baseline of the measured
curve can be specified.

[0073] As has been described above, if peaks are seen in the positive Y
direction, by scanning a semicircle or semi-ellipse at any position on
the X-axis about the reference point (xi, 0), the minimum values
lXi-r(xi)min to lXi+r(xi)min of difference
in height between the spectrum and the figure at individual positions of
the figure (having its center in the range of (xi-r) to (xi+r))
are added to the height fXi-r(xi) to fXi+r(xi) at the
reference point (xi, 0) of the individual positions of the figure,
and

are obtained. The maximum value L.sub.(xi) of the sum is obtained as a
baseline value. The reference point is moved in the X direction, and the
other baseline values are obtained by following the procedure as
described above. By this simple method, a highly accurate baseline can be
created automatically. Here, the figure should be moved in the X
direction alone. Since complicated movements are not required, the
computational load is low.

[0074] By adjusting the value of "r" to make the X radius R of the
semicircle twice the full width at half maximum of a peak having the
greatest peak width or greater, even if there is a peak at point
(xi, 0) on the X-axis, where the baseline point is going to be
specified, the difference in height between the spectrum and the figure
is calculated as the minimum value l(xi)min at an off-peak
X-axis position. Then, the figure is moved as described above,
lXi-r(xi)min to lXi+r(xi)min are
calculated, and the values are incorporated in the following calculation:

Since the values of lXi-r(xi)min to
lXi+r(xi)min are the differences in height between the
spectrum and the figure at off-peak positions, they do not become too
large, and L.sub.(xi) is set to an appropriate value.

[0075] If the spectrum rises toward the right, rises toward the left,
rises in the middle, falls in the middle, or is wavy, an appropriate
baseline can be obtained by adjusting the values of curvature "a" and
radius "r" in accordance with the shape and inclination of the entire
spectrum and the width of the peak.

[0076] When a quadratic curve is used, a quadratic curve D having its
vertex at point (xi, c) (xi=b at the beginning of the
measurement) is formed under the following conditions

f(x)=a(x-b)2+c

b-M≦x≦b+M

M≧W

a<0 (if peaks are seen in the positive Y direction)

where W is the full width at half maximum of a peak having the greatest
peak width among a plurality of peaks appearing in the measured curve,
and a baseline is formed by following the procedure described above. By
this simple method, a highly accurate baseline can be created
automatically.

[0077] The values of "b" and "c" are specified as the initial position (b,
c) of the quadratic curve.

[0078] The figure should be moved in the X direction alone. Since
complicated movements are not required, the computational load is low.

[0079] If the figure such as a semicircle is moved along the spectrum, the
complicated movement of the figure would require manual intervention.
According to the present invention, the figure should be moved in the X
direction alone. The baseline can be set through a very simple operation.
After the initial parameters are specified, the baseline is set almost
automatically without any other manual intervention.

BRIEF DESCRIPTION OF THE DRAWINGS

[0080] FIG. 1 illustrates the calculation of Ymint+fXi(Xi)
with a semicircle centered at a reference point (Xi, 0), when peaks
are seen in the positive Y direction.

[0081] FIG. 2 illustrates the calculation of
Ymin(t+1)+fXi+d(Xi) with a semicircle centered at point
(Xi+d, 0) while the reference point is (Xi, 0), when peaks are
seen in the positive Y direction.

[0082] FIG. 3 illustrates the calculation when the center of the
semicircle is moved in the range of (Xi-r, 0) to (Xi+r, 0)
while the reference point is (Xi, 0), when peaks are seen in the
positive Y direction.

[0083] FIG. 4 illustrates the setting of baseline points by moving the
reference point and using a semicircle at the reference point in
accordance with a baseline setting method according to the present
invention, when peaks are seen in the positive Y direction.

[0084] FIG. 5 illustrates the position of Ymin when the baseline is
set by using a semicircle (y≦0), if peaks are seen in the negative
Y direction.

[0085] FIG. 6 illustrates the calculation when the center of the
semicircle (y≦0) is moved in the range of (Xi-r, 0) to
(Xi+r, 0) while the reference point is (Xi, 0), if peaks are
seen in the negative Y direction.

[0086]FIG. 7 shows the correspondence between positions of the figures
and points plotted in FIG. 6, where the value of Ymin is subtracted
from the height of each figure at the reference point (Xi, 0), and
the calculated difference is plotted as height on x=Xi.

[0087] FIG. 8 shows an example of a baseline setting method according to
the present invention, by using a semicircle.

[0088] FIG. 9 shows an example of baseline setting by using a line
segment, and by adjusting the position of the line segment according to
the method of the present invention.

[0089] FIG. 10 shows an example of the baseline setting method according
to the present invention, by using a spectrum differing from that used in
FIG. 8 and a semicircle.

[0090] FIG. 11 shows an example of baseline setting by using a spectrum
differing from that used in FIG. 9 and a line segment, and by adjusting
the position of the line segment according to the method of the present
invention.

[0091] FIG. 12 shows an example of a baseline setting method according to
the present invention, by using a semicircle, when peaks are seen in the
negative Y direction.

[0092] FIG. 13 illustrates the calculation of Ymin in the baseline
setting method according to the present invention, by using a semicircle
with its circumference intersecting the measured curve.

[0093] FIG. 14 illustrates the calculation of Ymin1+fXi(Xi)
with a quadratic curve having its vertex at a reference point (Xi,
0), when peaks are seen in the positive Y direction.

[0094] FIG. 15 illustrates the calculation of
Ymin2+fXi+d(Xi) with a quadratic curve having its vertex
at point (Xi+d, 0) while the reference point is (Xi, 0), when
peaks are seen in the positive Y direction.

[0095] FIG. 16 illustrates the setting of a baseline point by moving the
reference point and using a quadratic curve at the moved reference point
in accordance with the baseline setting method according to the present
invention, when peaks are seen in the positive Y direction.

[0096] FIG. 17 illustrates the calculation of fXi(Xi)+Ymin1
in an initial position (b, c) of the vertex of a quadratic curve D, the
initial position being aligned with the x coordinate of a peak of a
spectrum and the height of the peak, while the reference point is (Xi,
0).

[0097] FIG. 18 illustrates the calculation of
fXi+r(Xi)+Ymin2 when the quadratic curve D is moved from
the initial position (b, c) of the vertex by distance "r" in the X
direction, the initial position being aligned with the x coordinate of
the peak of the spectrum and the height of the peak, while the reference
point is (Xi, 0).

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0098] With reference to FIGS. 1 to 4, a procedure for setting a baseline
by using a semicircle at point (X, 0) when peaks are seen in the positive
Y direction will be described.

[0099] With reference to FIGS. 5 to 7, a baseline point setting process
according to the present invention, when the peaks are seen in the
negative Y direction, will be described.

[0100] FIGS. 8 to 11 show baselines specified by using a line or
semicircle. The baselines specified by using a semicircle or line will be
compared while the adjustment of "a" is described.

[0101] FIG. 12 shows an example in which the baseline is specified by
using a semicircle and the spectrum is baseline-corrected, when peaks are
seen in the negative Y direction.

[0102] FIG. 13 illustrates a spectrum intersecting a semicircle having a
large diameter.

[0103] With reference to FIGS. 14 to 16, a procedure for setting a
baseline by using a quadratic curve with its vertex at point (X, 0) will
be described.

[0104] FIGS. 17 and 18 show an example in which the initial position (b,
c) of the vertex of a quadratic curve D is aligned with the x coordinate
of a peak of the measured line and the height of the peak.

[0105] As a first embodiment of the present invention, a procedure for
setting a baseline by using a semicircle when peaks are seen in the
positive Y direction will be described with reference to FIGS. 1 to 4.

[0106] The operator first specifies a circle or ellipse with its center at
point (Xi, 0).

[0107] The circle or ellipse is expressed by

X2+a2Y2=r2

(f(x)={(r2-x2)1/2}/a)

and set by specifying the values of curvature "a" and radius "r".

[0108] The values of "a" and "r" of the circle or ellipse are specified
empirically. It is preferable to set the X radius R of the semicircle or
semi-ellipse C to twice the full width at half maximum, W, or greater,
where W is the full width at half maximum of a peak having the greatest
peak width among a plurality of peaks appearing in the measured curve, so
that baseline points are set in an appropriate height.

[0109] From the spectrum S at each point in the horizontal axis region
containing the figure, a measured value S at (x, 0) in the range of
(Xi-r, 0) to (Xi+r, 0) is compared with
{(r2-x2)1/2}/a (y≧0) to calculate the difference Y
between them:

Y=(S-{(r2-x2)1/2}/a).

[0110] Then, the minimum value Ymint of Y is calculated.

[0111] The calculated Ymint is added to the height fxi(Xi)
of the figure at point (Xi, 0) to obtain (see FIG. 1)

Ymint+fxi(Xi).

[0112] The figure is moved by "d" parallel to the X-axis within a range
including point (Xi, 0).

[0113] From the spectrum at each point in the horizontal axis region
containing the figure, a measured value "S" in the range of (Xi+d-r,
0) to (Xi+d+r, 0) is compared with {(r2-x2)1/2}/a
(y≧0) to calculate the difference Y between them:

Y=(S-{(r2-x2)1/2}/a).

[0114] Then, the minimum value Ymin(t+1) of Y is calculated.

[0115] The calculated Ymin(t+1) is added to the height
fXi+d(Xi) of the figure at point (Xi, 0) to obtain (see
FIG. 2)

Ymin(t+1)+fxi+d(X1).

[0116] By repeating this step while moving the figure within the range of
(X-r, 0) to (X+r, 0), the following are calculated:

From the results, the maximum value P1 is selected. A baseline point
(Xi, P1) at (Xi, 0) is specified (FIG. 3).

[0117] In FIG. 3, a peak on the measured curve is on the reference point
(Xi, 0), but Ymin is set in an off-peak position in each of the
five shown semicircles (Ymin values are calculated separately for
the individual circles). By calculating

and selecting the maximum value P1, the baseline point (Xi,
P1) is set to an appropriate height.

[0118] By moving the point (Xi, 0) in the X direction and repeating
the same steps for point (X.sub.(i+1), 0), the maximum value P2 is
set as a baseline point at point (X.sub.(i+1), 0).

[0119] The same procedure is repeated to calculate baseline points P at
(Xi, 0), (X.sub.(i+1), 0), to (X.sub.(i+n-1), 0). By connecting those
points, a baseline BL is obtained (FIG. 4).

[0120] The present invention can also be used when peaks are seen in the
negative Y direction. The procedure differs from the procedure when peaks
are seen in the positive Y direction, and a supplementary description
will be added.

[0121] When peaks are shown in the negative Y direction, a semicircle must
be specified in the range of y≦0, as shown in FIG. 5.

[0122] Moreover, Ymin should be taken from a position where the
absolute value of the distance between the circumference of the circle
and the spectrum is the greatest. So, Ymin is set to f(x)-S, where f(x)
is the value of height of the figure, and S is a measured value.

[0123] The height of the figure at (Xi, 0) is expressed as
f(xi), as shown in FIG. 6. While the figure is moved in the X
direction, the following is obtained:

[0124] In FIG. 6, a plurality of points are plotted, and the minimum value
fXi+1/2r(xi)-Yminj becomes a baseline point.

[0125]FIG. 7 shows arrows indicating the correspondence between the
points plotted in FIG. 6 and circles.

[0126] If the specimen emits light in absorbance measurement with an FT-IR
or ultraviolet-visible photometer, the amount of light reaching the
detector increases, decreasing the absorbance. In Raman scattering
intensity measurement using a Raman spectrometer, if the specimen emits
light, the spectrum can be raised.

[0127] In those cases, baseline correction using a circle, as shown in
FIG. 8 or 10, can scale down the vertical axis, making it possible to
detect a small peak that would not be detected on the previous scale of
the vertical axis. Accordingly, the hit ratio in a library search can be
improved.

[0128] For the comparison, FIGS. 9 and 11 show examples of baseline
setting where a figure is adjusted according to the present invention,
and a line segment is used.

[0129] (1) FIG. 8 shows an example using a circle, and FIG. 9 shows an
example using a line segment, given for comparison. Although the baseline
setting by using a line segment is not included in the scope of the
present invention, it can be regarded as an example using an ellipse
having a very small Y diameter because F(x), or the ellipse having a very
small Y diameter, is close to a line segment.

[0130] The spectra shown in FIGS. 8(a) and 9(a) are rising toward the
left.

[0131] The scale of the Y-axis after baseline correction in FIG. 9(b) is
smaller than that in FIG. 8(b).

[0132] That is because the baseline in FIG. 9(a) is parallel to the X-axis
around a peak of the spectrum appearing in the range of 2800 to 3000
(cm-1).

[0133] The baseline-corrected spectrum seen in the range of 2800 to 3000
(cm-1) in FIG. 9(b) has a narrower shape than that in FIG. 8(b), and
the corrected spectrum has a missing part. Therefore, it is understood
that the baseline in FIG. 9(b) is inappropriate.

[0134] (2) FIG. 10 shows an example using a circle, and FIG. 11 shows an
example using a line segment, given for comparison.

[0135] The baseline shown in FIG. 11(a) has a part parallel to the X-axis
in the range of 500 to 1700 [cm-1], and the shape of the
baseline-corrected spectrum differs from that in FIG. 10(b).

[0136] Like the spectrum shown in FIG. 9(b), the baseline-corrected
spectrum in FIG. 11(b) has a missing part. An ideal baseline provides a
spectrum without a missing part, as shown in FIG. 10(a).

[0137] FIG. 12 shows an example of baseline setting according to the
present invention, where a semicircle is used when peaks are seen in the
negative Y direction.

[0138] The upper graph in FIG. 12 shows peaks in the negative Y direction
and a spectrum declining toward the right. After baseline correction
according to the present invention, the vertical axis representing
transmittance (% T) is scaled down, and the peaks of the spectrum are
emphasized.

[0139] FIG. 13 shows a case where the circumference of a circle intersects
a measured curve.

[0140] When peaks are seen in the positive Y direction, if f(x)
(={(r2-x2)1/2}/a) (y≧0) is greater than a specific
point yi on the measured curve, l(xi)min [=yi-f(x)]
becomes a negative value. Even in that case, the maximum value of

is selected as L.sub.(xi), and a baseline point (xi, L.sub.(xi)) can
be calculated normally in the same procedure.

[0141] As a second embodiment of the present invention, a procedure for
setting a baseline by using a quadratic curve will be described with
reference to FIGS. 14 to 16.

[0142] If peaks are seen in the positive Y direction, the operator first
specifies a quadratic curve having its vertex at point (Xi, 0),
under the following conditions:

f(x)=a(x-b)2+c

b-M≦x≦b+M

M≧W

a<0

where W is the full width at half maximum of a peak having the greatest
peak width among a plurality of peaks appearing in the measured curve.

[0143] The quadratic curve expressed by

y=a(x-b)2+c

(f(x)=a(x-b)2+c)

is set by specifying the values of "a", "b", and "c".

[0144] The parameter "a" of the quadratic curve is set empirically, with
the width of the peak taken into account. If peaks are seen in the
positive Y direction, however, the value of "a" should be negative. The
value of M is specified to satisfy W≦M, where W is the full width
at half maximum of a peak having the greatest peak width among a
plurality of peaks appearing in the measured curve. The range of the
quadratic curve must be specified by setting the following:

b-M≦x≦b+M

The initial position (b, c) of the vertex of the quadratic curve is also
specified.

[0145] In the second embodiment, "c" is set to zero (hereafter
f(x)=a(x-b)2), but "c" is not confined to zero.

[0146] If peaks of the measured curve are seen in the negative Y
direction, the value of "a" should be positive.

[0147] From the spectrum at each point in the horizontal axis region
containing the figure, the measured value S in the range of (Xi-M,
0) to (Xi+M, 0) and the height a(x-b)2 of the figure in that
position are obtained to calculate the difference Y between them:

Y={S-a(x-b)2}.

[0148] The minimum value Ymin1 of Y is calculated next.

[0149] The height fXi(Xi) of the figure at point (Xi, 0) is
added to Ymin1 to obtain (see FIG. 14)

Ymin1+fXi(X1).

[0150] If peaks are seen in the negative Y direction,

Y={a(x-b)2-S}

is obtained, and the minimum value of Y should be set as Ymin1.

[0151] The figure is moved by "d" parallel to the X-axis within the range
including point (Xi, 0).

[0152] From the spectrum at each point in the horizontal axis region
including the figure, a measured value S in the range of (Xi+d-M, 0)
to (Xi+d+M, 0) is compared with the height a(x-b)2 of the
figure in that position to calculate the difference Y between them:

Y={S-a(x-b)2}.

[0153] The minimum value of Y is calculated as Ymin2.

[0154] The height fXi+d(Xi) of the figure at point (Xi, 0)
and Ymin2 are added to obtain (see FIG. 15)

[0158] Point (Xi, 0) is moved in the X direction, the same operation
is performed at point (X.sub.(i+1), 0), and the maximum value P2 is
specified as a baseline point at point (X.sub.(i+1), 0).

[0159] By repeating this operation, baseline points P at points (Xi,
0) through (X.sub.(i+1), 0) to (X.sub.(i+n-1), 0) are calculated. By
connecting those points, a baseline BL is obtained (FIG. 16). FIG. 16
shows three baseline points (X1 to X3), but more points are
plotted in practice.

[0160] FIGS. 17 and 18 show examples in which the initial position (b, c)
of the vertex of a quadratic curve D is aligned with the height of the
peak and the x coordinate of the peak of the spectrum. The quadratic
curve shown in FIG. 18 has been moved by distance "r" in the X direction
from the position shown in FIG. 17.

[0161] If f(x) (=a(x-b)2+c) is greater than a specific point yi
on the measured curve, the value of l(xi)min [=yXi-f(x)]
becomes negative. Even in that case, the maximum value of